WASHINGTON — Cecile Richards, the president of Planned Parenthood Federation of America, was poring over a spiral notebook in her bare-bones office here when she was asked about President Trump’s latest attempt to cut a deal on abortion.

Days earlier, the Trump White House had floated a trial balloon: If Planned Parenthood would quit performing abortions, it could keep roughly $550 million in annual federal funding.

Ms. Richards, 59, a savvy former political organizer (and a daughter of former Gov. Ann Richards, the tough-talking Texas Democrat) scowled, wondering aloud if the proposal was even serious. “That is just not going to happen,” she said flatly. “We would never abandon the women who count on us in exchange for cash.”

But while Ms. Richards stands at the forefront of efforts to protect access to abortion, another politically savvy woman, Marjorie Dannenfelser, who helped elect Mr. Trump and is a longtime ally of Vice President Mike Pence, is just as ardently on the other side, pushing hard to prevent Planned Parenthood from getting a single penny from taxpayers.

This week, she had reason to celebrate: Mr. Pence cast the tiebreaking vote when the Senate rolled back an Obama administration rule barring states from denying family planning grants to Planned Parenthood and other abortion providers. The bill will now go to Mr. Trump’s desk.

“This is the result of decades of work, to defund this organization we think is evil,” said Ms. Dannenfelser, 51, president of Susan B. Anthony List, an anti-abortion group. During last year’s presidential campaign, she agreed to back Mr. Trump (who in 1999 described himself as “very pro-choice”) in exchange for his written promise that he would pursue an anti-abortion agenda — including “nominating pro-life justices” to the Supreme Court, and stripping Planned Parenthood of federal funding if the group continues to provide abortions.

Days after their January inaugural, Mr. Pence hosted a cheese-and-crackers reception for movement leaders in his ceremonial office — an event Ms. Dannenfelser described as a homecoming.

“Cecile Richards was in the White House all the time during the Obama administration,” she said. “Now it’s our turn.”

These are challenging times for Planned Parenthood, the reproductive rights behemoth known to millions of American women as the place to turn for cancer screening, testing for sexually transmitted diseases, birth control — and yes, abortion. A century after its founder, the pioneering sex educator Margaret Sanger, committed the radical act of opening a birth control clinic in Brooklyn — only to have it shut down by the police — Planned Parenthood had expected to mark its centennial with a big gala in May and Hillary Clinton in the White House.

Instead, Mr. Trump’s election has given new life to the abortion wars in Washington, and thrust Ms. Richards — and women, many of them poor, across America who rely on Planned Parenthood for basic health care — into a pitched battle with the president. Mr. Trump lost badly in the first round, when the Republican effort to replace the Affordable Care Act fell apart last month on Capitol Hill. The measure would have barred Medicaid dollars, for one year, from going to any family planning center that provides abortions.

There is only one group that fits that description: Planned Parenthood.

“The goal here is they want to end access to safe and legal abortion in America,” Ms. Richards said, “and the way they do that is by going after Planned Parenthood.”

The health measure would have been far more damaging to Planned Parenthood than the one the Senate just passed and in the weeks leading up to the vote, Ms. Richards led a massive effort to defeat it.

Planned Parenthood says its supporters made 122,000 phone calls to members of Congress and organized more than 1,000 events around the nation, including rallies, petitions, phone banks and marches, carefully targeted to Republican moderates. On the day of the vote, 75 supporters showed up at the Northern Virginia offices of Representative Barbara Comstock, a Virginia Republican. A half-hour later, she announced that she would oppose the health bill.

Ms. Richards also traveled the country visiting clinics, including in Wisconsin, the home state of the House speaker, Paul D. Ryan, the chief architect of the health measure. (There are three Planned Parenthood clinics in his district alone.) Hundreds of women, dressed in pink, turned out for a rally in Milwaukee, where Ms. Richards instructed them to deliver a pointed message to the speaker:

“You need to let him know that people in Wisconsin deserve the same ability to choose their doctors as he and every member of Congress have.”

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Vice President Mike Pence speaking at an anti-abortion rally in Washington, a week after the inauguration. Mr. Pence, a social conservative, is regarded as a hero in the anti-abortion movement.CreditAl Drago/The New York Times

Abortions are only a small part of Planned Parenthood’s business, and Medicaid does not pay for them. The federal Hyde Amendment bars tax dollars from financing abortions except in cases of incest, rape or when the health of the mother is at risk. But for Planned Parenthood, which receives roughly 43 percent of its $1.3 billion in annual revenue from the federal government, the loss of Medicaid dollars could be crippling. There is no question that clinics would be forced to close as a result.

As a guide, experts look to Texas. In 2011, the state Legislature slashed its two-year budget for family planning to $38 million from $111 million in an effort to defund Planned Parenthood. After those cuts, one quarter of all Texas family planning clinics closed, according to a study by the Population Research Center at the University of Texas.

With more than 650 health centers around the country — in every state except North Dakota — Planned Parenthood sees about 2.5 million patients a year, roughly 1.6 million of them through Medicaid, according to Dr. Raegan McDonald-Mosley, its chief medical officer. Screening for sexually transmitted infections is the No. 1 reason patients visit, and birth control is also high on the list.

While the Obamacare repeal bill is off the table, for now, the fight over Planned Parenthood is not over. It could come up again next month; Republicans may try to attach the defunding provision to a bill financing government operations for the rest of the year. Or, Ms. Dannenfelser and other anti-abortion movement leaders say their Republican allies on Capitol Hill could tack it on to another measure, possibly a tax reform bill, this the spring.

The anti-abortion movement has set its sights on Planned Parenthood for years — at least since 2007, when Mr. Pence, then an Indiana congressman, introduced the first measure to defund the organization. (“We are truly fellow travelers,’’ Ms. Dannenfelser said of the vice president.) His bill went nowhere, but the idea quickly gained traction inside the anti-abortion movement, said Kristan Hawkins, president of Students for Life, which organizes abortion opponents on college campuses.

In 2012, Ms. Hawkins said, her group commissioned Kellyanne Conway, the pollster who is now a senior adviser to Mr. Trump, to research abortion opponents’ attitudes toward Planned Parenthood. “We had all these people who said they were pro-life, who didn’t know what Planned Parenthood was, and didn’t know they committed abortions,” she said.

Ms. Hawkins set out to change that, and by 2013, her group was touring college campuses, carrying pink banners and 888 pink crosses to represent the number of abortions performed each day by Planned Parenthood. (The number is derived from Planned Parenthood’s annual report; its clinics performed just under 324,000 abortions last year; abortions account for just 3 percent of the medical services the group provides.)

Then, in 2015, undercover anti-abortion activists released a series of graphic videos purportedly showing Planned Parenthood officials discussing the sale of fetal body parts — a move that spurred the Republican leadership in the Senate to push a defunding measure. (Last week, California prosecutors charged two of the undercover activists with 15 felonies, saying that they had invaded the privacy of medical providers while misrepresenting themselves as they sought to buy fetal tissue from Planned Parenthood.)

The videos were a turning point, said Senator James Lankford, an Oklahoma Republican and a staunch abortion opponent. He said constituents did not want their money going to any group that performs abortions.

“There is a firm belief by many, myself included, that would say ending a life is not health care,’’ he said.

The bill passed, but was vetoed by President Barack Obama. With Mr. Trump in the White House, “the threat is very real and there’s no one to veto this,” said Anita Dunn, Mr. Obama’s former communications director, whose strategy firm now consults for Planned Parenthood.

For the president, a latecomer to the anti-abortion movement, the politics around Planned Parenthood are complicated. For one thing, public support for Planned Parenthood is high; a recent survey by the Kaiser Family Foundation found that three-quarters of respondents — including a majority of Republican women and men — backed continuing Medicaid funding to pay for “nonabortion services,” while just 22 percent supported cutting off all federal funding.

Mr. Trump’s daughter Ivanka is said to be a strong supporter of the organization, which is one reason the Trump White House may have floated the possible deal. Ms. Richards said no one from the White House approached her directly with the proposal, and there was never any serious debate about whether to accept it.

Mr. Trump has his own statements to contend with. During the campaign, he broke with fellow Republicans in sounding supportive of Planned Parenthood.

“I would defund it because I’m pro-life,” Mr. Trump said during a debate on CNN in February 2016, “but millions of women are helped by Planned Parenthood.”

Ms. Richards is soldiering on. She was asked what her mother, whose lacerating one-liners made her a feminist icon in her day, might say. “I think the main thing she would say is, ‘Quit whining and get back to work. This is not a time to wring your hands.’”

Correction:

An earlier version of this article misstated the number of abortions performed by Planned Parenthood clinics last year. It was 324,000 not 234,000.